Question

In triangle abc ,given that ab = ac and bd is perpendicular to ac .prove that bc^2=2 AC.CD....​

Answer 1

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rajeevgupta39

Secondary SchoolMath 5+3 pts

Isosceles triangle ABC with AB=AC and BD perpendicular to AC ,prove that BC^2=2AC.CD

Comments (2) Report by Abhishekcpr 27.02.2018

manishmaxy

what to prove can u tell me clearly

abhishekcpr

prove that BC square=2AC.CD

Answers

rajeevgupta39

Rajeevgupta39 · Ace

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harsh1234567892

Harsh1234567892 Expert

here's your ans

In Δ BCD by pythagoras theorem, we have

⇒ BC2 = BD2 + CD2 ... (1)

Again, in Δ ABD by pythagoras theorem

AB2 = BD2 + AD2

⇒ BD2 = AB2 - AD2

On putting value of BD2 in (1), we get

BC2 = AB2 - AD2 + CD2

⇒ BC2 = AB2 - (AC - CD)2 + CD2

⇒ BC2 = AB2 - AC2 - CD2 + 2AC. CD + CD2

⇒ BC2 = 2AC. CD [Given, AB = AC. ⇒ AB2 = AC2]

Proved

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